Numerical weather prediction is a fascinating subject and a paradigm for modern applied science. It has also been the cradle of modern scientific computing: the first numerical solution of a partial differential equation on an electronic computer was computed in the attempt to produce a numerical weather forecast. Even before that, the vision of L.F. Richardson put the power of mathematical modelling and approximation theory to work, in order to solve a problem of apparently unlimited complexity. One century after Richardson's first attempts, numerical weather prediction is still one of the most advanced areas of applied research and technology.

My own contribution to numerical weather prediction has focused on three main areas:

• Finite volume description of the orography to replace adapted vertical coordinates

• Development of the earlier versions of the ICON model and analysis of mimetic finite difference methods for atmospheric flows employed in these ICON versions

• Efficient Discontinuous Galerkin methods based on semi-implicit, semi-Lagrangian and adaptive approaches. These ideas have been included in the prototype models developed in the ESCAPE-2 project.